University:
East Georgia State College
Course:
MATH 1113 | Pre-Calculus
Academic year:

2023
Views:

345

Pages:

4
Author:

Clint W.

Translate and Reflect Trigonometric Graphs Algebra 2 CP 14.2 Notes Name________________ Date_________________ Warm up – Identify the vertex of the parabola 1. 2. 3. 4. 5. Translations of Sine and Cosine Graphs y = asin b(x – h) + k y = acos b(x – h) + k h = horizontal shift , k = vertical shift if a is negative then the graph will reflect 2 b 1. Find the amplitude, a and period, 2. Graph the parent function without any shifts (from 14.1) 3. Identify the “new” origin using (h,k) 4. Draw a dashed line for the midline (your new x-axis), and then one below and above for amplitude. Draw a vertical dashed line to represent the horizontal shift (your new y-axis) 5. The dashed lines represent your new graph, now plot the same way that you did from step 2! EXAMPLE 1 – Graphing a Vertical Translation Graph the parent function and the given function on the same set of axes. a. y  sin x  4 b. 1 y  cos 2 x  2 2 EXAMPLE 2 – Graphing a Horizontal Translation Graph the parent function and the given function on the same set of axes. a. y  sinx  3  b. 1  y  3sin  x   2 2 c. y  cosx     1 EXAMPLE 3 – All Shifts, Reflections, and Transformations Graph the parent function and the given function on the same set of axes. a. 1  y  4 cos  x   3 2 b. y  cos 2x  2   3 c. y   cosx    d. 1 y  3sin x  2 2 EXAMPLE 4 – Writing Transformation Equations Write an equation of the graph described below.  units a. The graph of y = cos x is translated up 3 units and right b. The graph of y = cos 2  x is translated down 4 units and left c. The graph of y = sin d.  2  2 units x is reflected The graph of y = 3cos  x is reflected, shifted 7 units down and 5 units left

Math Translsate and Reflect Trigonometric Graphs

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